On perfectly matched layers for discontinuous Petrov-Galerkin methods

TL;DR

This paper develops and analyzes discontinuous Petrov-Galerkin methods with perfectly matched layers for wave propagation in unbounded domains, introducing new formulations and demonstrating their effectiveness through numerical experiments.

Contribution

It introduces novel DPG formulations with PMLs using complex coordinate stretching, enhancing wave simulation accuracy in unbounded domains.

Findings

New DPG methods with PMLs are effective for wave problems.

Different complex stretching strategies lead to distinct formulations.

Numerical results confirm the methods' efficacy.

Abstract

In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formulations used by Bubnov-Galerkin methods, with so-called ultraweak variational formulations, these two strategies in fact deliver different formulations in the PML region. One of the strategies, which is argued to be more physically natural, is employed for numerically solving two- and three-dimensional time-harmonic acoustic, elastic, and electromagnetic wave propagation problems, defined in unbounded domains. Through these numerical experiments, efficacy of the new DPG methods with PMLs is verified.